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We present an approach to the admission control and resource allocation problem in connection-oriented networks that offer multiple services to users. users' preferences are summarized by means of their utility functions, and each user is allowed to request more than one type of service. Multiple types of resources are allocated at each link along the path of a connection. We assume that the relation between Quality of Service (QoS) and resource allocation is given, and we incorporate it as a constraint into a static optimization problem. The objective of the optimization problem is to determine the amount of and required resources for each type of service to maximize the sum of the users' utilities. We prove the existence of a solution of the optimization problem and describe a competitive market economy that implements the solution and satisfies the informational constraints imposed by the nature of the decentralized resource allocation problem. The economy consists of four different types of agents: resource providers, service providers, users, and an auctioneer that regulates the prices based on the observed aggregate excess demand. The goods that are sold are: (i) the resources at each link of the network, and (ii) services constructed from these resources and then delivered to users. We specify an iterative procedure that is used by the auctioneer to update the prices, and we show that it leads to an allocation that is arbitrarily close to a solution of the optimization problem in a finite number of iterations.